Average Error: 0.5 → 0.5
Time: 2.7s
Precision: 64
\[\sqrt{x - 1} \cdot \sqrt{x}\]
↓
\[\sqrt{x - 1} \cdot \sqrt{x}\]
\sqrt{x - 1} \cdot \sqrt{x}
↓
\sqrt{x - 1} \cdot \sqrt{x}
double f(double x) {
        double r6724 = x;
        double r6725 = 1.0;
        double r6726 = r6724 - r6725;
        double r6727 = sqrt(r6726);
        double r6728 = sqrt(r6724);
        double r6729 = r6727 * r6728;
        return r6729;
}
↓
double f(double x) {
        double r6730 = x;
        double r6731 = 1.0;
        double r6732 = r6730 - r6731;
        double r6733 = sqrt(r6732);
        double r6734 = sqrt(r6730);
        double r6735 = r6733 * r6734;
        return r6735;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.5

    \[\sqrt{x - 1} \cdot \sqrt{x}\]

  2. Final simplification0.5

    \[\leadsto \sqrt{x - 1} \cdot \sqrt{x}\]

Reproduce

herbie shell --seed 2020020 +o rules:numerics
(FPCore (x)
  :name "sqrt times"
  :precision binary64
  (* (sqrt (- x 1)) (sqrt x)))